- #1
titasB
- 14
- 2
Homework Statement
Find ∫ f(x) dx between [4,8]
if,
∫ f(2x) dx between [1,4] = 3 and ∫ f(x) dx between [2,4] = 4
Homework Equations
[/B]
∫ f(x) dx between [4,8] ,
∫ f(2x) dx between [1,4] = 3 and ∫ f(x) dx between [2,4] = 4
The Attempt at a Solution
We are given ∫ f(2x) dx between [1,4] = 3
Let, 2x = u ⇒ dx = du/2
So, the new intervals are u2 = 2(4) = 8 and u1 = 2(1) = 2
This gives: 1/2 ∫ f(u) du between [2,8] = 3 ⇒ ∫ f(u) du between [2,8] = 6
And so to find t ∫ f(x) dx between [4,8]
I subtract ∫ f(x) dx between [2,4] from ∫ f(2x) dx between [1,4]
which is the same as writing: ∫ f(u) du between [2,8] - ∫ f(x) dx between [2,4] = 6- 4 = 2
Is this the correct answer? I'm not sure if ∫ f(u) du between [2,8] = 6 is the same as ∫ f(x) dx between [2,8] = 6
I read something about a dummy variable and this seems like a reasonable answer. Please let me know.